To do this, you would simple download the parts via ant, eclipse or some other development tool. Then create a new git repo and push that new repo to bitbucket.
These should get you started. The "trickiest" part is pulling down your code. You can do this with the Force.com IDE [1], Solenopsis [2], MavensMate [3] or using the ant tool chain directly [4]. As for using git, I'd recommend reading over this post [5]. It is geared towards distributed teams but the principles can be used for single person teams.
One thing I would recommend is that you do not make the root of your git repo a directory with all of your objects/pages/classes/etc. Instead create a src directory that contains those. This can help with storing additional data such as scripts or documentations.
Thanks
One thing I would recommend is that you do not make the root of your git repo a directory with all of your objects/pages/classes/etc. Instead create a src directory that contains those. This can help with storing additional data such as scripts or documentations.
Example file tree
[1] https://developer.salesforce.com/page/Force.com_IDE
[2] http://solenopsis.org/Solenopsis/
[3] http://mavensmate.com/
[4] http://www.salesforce.com/us/developer/docs/apexcode/Content/apex_deploying_ant.htm
[5] http://blog.deadlypenguin.com/blog/2014/07/21/using-git-with-salesforce-and-distributed-teams/